Previous |  Up |  Next


Title: A boundary multivalued integral “equation” approach to the semipermeability problem (English)
Author: Haslinger, Jaroslav
Author: Baniotopoulos, C. C.
Author: Panagiotopoulos, Panagiotis D.
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 38
Issue: 1
Year: 1993
Pages: 39-60
Summary lang: English
Category: math
Summary: The present paper concerns the problem of the flow through a semipermeable membrane of infinite thickness. The semipermeability boundary conditions are first considered to be monotone; these relations are therefore derived by convex superpotentials being in general nondifferentiable and nonfinite, and lead via a suitable application of the saddlepoint technique to the formulation of a multivalued boundary integral equation. The latter is equivalent to a boundary minimization problem with a small number of unknowns. The extension of the present theory to more general nonmonotone semipermeability conditions is also studied. Int the last section the theory is illustrated by two numerical examples. (English)
Keyword: approximations of unilateral BVP
Keyword: mixed and dual variational formulation of unilateral BVP
Keyword: semipermeable membrane
Keyword: infinite thickness
Keyword: convex superpotentials
Keyword: saddle-point technique
Keyword: boundary minimization problem
MSC: 35J85
MSC: 35R35
MSC: 49J40
MSC: 65N30
MSC: 76M30
MSC: 76M99
MSC: 76S05
idZBL: Zbl 0778.76092
idMR: MR1202079
DOI: 10.21136/AM.1993.104533
Date available: 2008-05-20T18:44:55Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] G. Duvaut, J. L. Lions: Les inéquations en Mécanique et en Physique.Dunod, Paris, 1972. Zbl 0298.73001, MR 0464857
Reference: [2] P. D. Panagiotopoulos: Inequality problems in Mechanics and applications. Convex and nonconvex energy functions.Birkhäuser Verlag, Basel/Boston, 1985. Zbl 0579.73014, MR 0896909
Reference: [3] J. Haslinger, P. D. Panagiotopoulos: The reciprocal variational approach to the Signorini problem with friction. Approximation results.Proc. Royal Soc. of Edinburgh 98 (1984), 250-265. Zbl 0547.73096, MR 0768357
Reference: [4] P. D. Panagiotopoulos: Multivalued boundary integral equations for inequality problems. The convex case.Acta Mechanica 70 (1987), 145-167. Zbl 0656.73038, MR 0922344, 10.1007/BF01174652
Reference: [5] P. D. Panagiotopoulos, P. P. Lazaridis: Boundary minimum principles for the unilateral contact problems.Int. J. Solids Struct. 23 (1987), 1465-1484. Zbl 0626.73123, MR 0918434, 10.1016/0020-7683(87)90064-3
Reference: [6] P. P. Lazaridis, P. D. Panagiotopoulos: Boundary variational "principles" for inequality Structural Analysis problems and numerical applications.Соmр. and Structures 25 (1987), 35-49. Zbl 0597.73096, MR 0880936, 10.1016/0045-7949(87)90216-1
Reference: [7] I. Hlaváček J. Haslinger J. Nečas, J. Lovíšek: Solution of variational inequalities in Mechanics.Springer Verlag, New York, 1988. MR 0952855
Reference: [8] P. D. Panagiotopoulos: A boundary integral inclusion approach to unilateral B.V.Ps in Elastostatics.Mech. Res. Comn. 10(1983), 91-93. Zbl 0508.73097, MR 0702788
Reference: [9] J. J. Moreau: La notion de sur-potentiel et les liaisons unilatérales en élastostatique.C. R. Acad. Sc. Paris 267A (1968), 954-957. Zbl 0172.49802, MR 0241038
Reference: [10] I. Ekeland, R. Temam: Convex Analysis and variational problems.American Elsevier, Amsterodam: North-Holland and New York, 1976. Zbl 0322.90046, MR 0463994
Reference: [11] F. H. Clarke: Optimization and Nonsmooth Analysis.Wiley, New York, 1983. Zbl 0582.49001, MR 0709590
Reference: [12] P. D. Panagiotopoulos: Nonconvex problems of semipermeable media and related topics.ZAMM 65 (1985), 29-36. Zbl 0574.73015, MR 0841254, 10.1002/zamm.19850650116
Reference: [13] K. C. Chang: Variational methods for non-differentiable functionals and their applications to partial differential equations.J. Math. Anal. Appl. 80 (1981), 102-129. Zbl 0487.49027, MR 0614246, 10.1016/0022-247X(81)90095-0
Reference: [14] P. D. Panagiotopoulos: Nonconvex energy functions. Hemivariational inequalities and substationarity principles.Acta Mechanica 42 (1983), 160-183. Zbl 0538.73018, MR 0715806
Reference: [15] J. J. Moreau P. D. Panagiotopoulos, G. Strang: Topics in Nonsmooth Mechanics.Birkhäuser Verlag, Basel/Boston, 1988. MR 0957086
Reference: [16] J. J. Moreau, P. D. Panagiotopoulos: Topics in Nonsmooth Mechanics and applications.CISM Lecture Notes, Vol. 302, Wien/New York, 1988. MR 0957086
Reference: [17] P. D. Panagiotopoulos, G. Stavroulakis: A variational-hemivariational inequality approach to the laminated plate theory under subdifferential boundary conditions.Quart. Appl. Math. XLVI (19SS), 409-430. MR 0963579
Reference: [18] J. Haslinger, I. Hlaváček: Convergence of a Finite element method based on the dual Variational Formulation.Apl. Mat. 21 (1976), 43-65. MR 0398126
Reference: [19] J. Nečas: Les methodes directes en teorie des équations elliptiques.Academia, Prague, 1967. MR 0227584
Reference: [20] J. L. Lions, E. Magenes: Problemes aux limites non homogenes.Dunod, Paris, 1968. Zbl 0165.10801
Reference: [21] J. Haslinger I. Hlaváček: Converges of a dual Finite element method in $R^n$.
Reference: [22] F. Brezzi W. Hegerand P. Raviart: Error Estimates for the Finite element solution of Variational Inequalities.Numer. Math. 28 (1979), 431-443. MR 0448949


Files Size Format View
AplMat_38-1993-1_5.pdf 1.749Mb application/pdf View/Open
Back to standard record
Partner of
EuDML logo